The elasticity of single flexible polymers using AFM based nanorheology*

The force versus extension curves generated by single molecule technique like AFM curves have been routinely used to describe the entropic elasticity of single polymer chains. These curves are typically modelled with an entropic worm-like chain model to estimate persistence length, a measure of local bending flexibility of chain. However, its estimated value is anomaly low and inconsistent  when measured with AFM in high force regime than with other techniques like Magnetic Tweezers in low force regime. To understand this, we performed AFM based experiments on Polyethylene glycol (PEG) polymer by oscillating the AFM cantilever probe externally through excitation of fixed frequency provided to it. We show that a proper quantification of elastic response measured locally and directly by oscillatory rheology technique deviates significantly from conventional force-extension curves. The persistence length obtained by WLC modelling of stiffness-extension data matches well with magnetic tweezers experiments. In addition, polystyrene chain in poor solvent show no deviation in elastic response between oscillatory technique and coventional constant velocity pulling experiments. However, such deviation was observed for polystyrene in good solvent. We attribute this to hydrophobic interaction between monomer units of polystyrene in water.

Our results suggest that oscillatory rheology provides a deconvolution between polymer intrinsic response and microscopic AFM cantilever probe and therefore correctly estimates elastic response.. The consistent values of persistence length estimated from  AFM experiments in high force regime and magnetic tweezers experiments in low force regime suggests that WLC is successful in describing the polymer elasticity across all force regime including force range typically probed in AFM experiments.